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The Health and Retirement Study is a longitudinal study of US adults enrolledat age 50 and older. We were interested in investigating the effect of a suddenlarge decline in wealth on the cognitive score of subjects. Our analysis wascomplicated by the lack of randomization, confounding by indication, and asubstantial fraction of the sample and population will die during follow-upleading to some of our outcomes being censored. Common methods to handle theseproblems for example marginal structural models, may not be appropriate becauseit upweights subjects who are more likely to die to obtain a population thatover time resembles that would have been obtained in the absence of death. Wepropose a refined approach by comparing the treatment effect among subjects whowould survive under both sets of treatment regimes being considered. We do soby viewing this as a large missing data problem and impute the survival statusand outcomes of the counterfactual. To improve the robustness of ourimputation, we used a modified version of the penalized spline of propensitymethods in treatment comparisons approach. We found that our proposed methodworked well in various simulation scenarios and our data analysis.

Accounting for selection bias due to death in estimating the effect of wealth shock on cognition for the Health and Retirement Study